Wind energy, part 2

Wind Energy, Part 2

Technical University of Eindhoven December 6, 2018 Gerard Schepers

ECN part of Tno/Hanze UAS Groningen

Gerard.schepers@tno.nl. +31 613100940

Contents

•

Principles of energy extraction, Betz-Lanchester

optimum

•

Design loads

•

Technology, state of the art

•

Wind Farm effects

•

Operation and Maintenance for Off-shore farms

What is a wind turbine:

A wind turbine transforms kinetic energy from the wind into mechanical (kinetic….) energy of the rotor(shaft)

Wind turbine Transformer Grid P_m = TΩ _P e = V I cosf Wind V(x,y,z,t) E_kin = ½ rV2 P_kin= ½ rV3_A E_kin = ½ rV2 P_kin= ½ rV3_A 3

4 5-2-2019 Figure: Modified from F. Grasso(ECN)

The axial force from the rotor on the air is a result of the

lift on the blade

Optimum energy extraction

•

_{Lanchester, Betz and Joukowsky showed}

independently (1916-1920) that optimum power

extraction is obtained when the wind speed at the

rotor disk is decelerated to 2/3 of its initial value

•

_{The relative reduction in wind speed at the rotor}

plane is called the

axial induction factor a.

So, an axial induction factor of 1/3 leads to optimal

power production

•

_{Then power extracted = 16/27 (~0.59) of free wind}

power (=1/2 ρ V

_w3

_A

R

)

•

_{This is known as the Betz maximum}

6 _5-2-2019

• The velocity in the rotor plane is reduced with the induced velocity

The induced velocity is V

_w

– V

_rotor

V_w

V_rotor

7 _5-2-2019

• The velocity in the rotor plane is reduced with the induced velocity

• Kinetic energy is extracted from the flow lower velocity in the rotor plane

The induced velocity is V

_w

– V

_rotor

V_w

V_rotor

8 _5-2-2019

• The velocity in the rotor plane is reduced with the induced velocity

• Kinetic energy is extracted from the flow lower velocity in the rotor plane

• The axial force from the rotor on the air ‘brakes’’ down the airflow lower velocity in the rotor plane

The induced velocity is V

_w

– V

_rotor

V_w

V_rotor

9 _5-2-2019

• The velocity in the rotor plane is reduced with the induced velocity

• Kinetic energy is extracted from the flow lower velocity in the rotor plane

• The axial force from the rotor on the air ‘brakes’’ down the airflow lower velocity in the rotor plane

• The induced velocity can be related to the power/energy

(conservation of energy) and to the axial force(conservation of momentum)

The induced velocity is V

_w

– V

_rotor

V_w

V_rotor

10 _5-2-2019

• The velocity in the rotor plane is reduced with the induced velocity

• Kinetic energy is extracted from the flow lower velocity in the rotor plane

• The axial force from the rotor on the air ‘brakes’’ down the airflow lower velocity in the rotor plane

• The induced velocity can be related to the power/energy

(conservation of energy) and to the axial force(conservation of momentum)

• Together with P = F_ax.V_rotorand conservation of mass the induced velocity is solved

The induced velocity is V

_w

– V

_rotor

V_w

V_rotor

The induced velocity is made non-dimensional:

The axial induction factor a

V_w

a is the relative induced velocity

V_rotor w induced w rotor w

V

u

V

V

V

a







V_wake

•

Power (energy/time) extracted from fluid:

– Scalar product of (negative) force vector on the flow and the velocity of the flow

•

However the main direction is axial so it is mainly the axial force

from the rotor on the flow (F

_ax (or D_ax or T from Thrust)

) and the

axial velocity component U

_d

( where index d denotes disc value)

P

_extracted

= - F

_ax

U

_d

•

The energy extraction from the rotor out of the flow will now

be approximated by assuming the rotor to be an actuator disk.

12

Fax

What is an actuator disc?

•An actuator disc is not ‘something real’ • It is a kind of porous disc, only

used to understand the process of the energy extraction

• Exerts axial force on air flow • Extracts power from flow

Constant pressure jump p over actuator disc

represents axial rotor force F_ax : p = F_ax / A_R with A_R the rotor area (=pR2₎

In general rotor theory:

The rotor is represented as an actuator disc

R

L. Lignaroli,

On the turbulent mixing in horizontal axis turbine wakes TUDelft, April 2016

Turbine

‘Actuator disc’

Momentum theory

Flow geometry: Sections 1, 4: far upstream resp. downstream

Sections 2, 3: just upstream resp downstream of actuator disk

A₁ A₄

Stream tube boundary

U_{1 =} V_{w U4} A_R U₂=U₃=U_d F_{ax Control volume} A₁ Actuator disc Sections: 1 2 3 4

Consider conservation laws on stream tube which contains actuator disc with axial force F_ax in uniform flow

Flow assumptions

• Homogeneous, incompressible and inviscid fluid

• Steady state flow

• Actuator disk is semi-transparent to flow: creates pressure discontinuity

• Uniform flow conditions over disk.

Axial force F_ax = (p₂ - p₃)A_R Power extracted: P_extracted = U_d (p₂ - p₃)A_R

Fluid dynamic conservation laws applied to stream

tube

1. Conservation of mass (per second through the streamtube)

2. Conservation of momentum 3. Conservation of energy m A U A U A U UA

r

_{1 1} 

r

_{d R} 

r

_{4 4}  

r



U U



Fax m U m U m ₁   ₄   ₁  ₄ 



U U



U U



FaxUd m _{  } 4 1 4 1 2  d axU F P U U m U m U m _{    } ) ( 2 2 2 2 4 2 1 2 4 2 1   

Velocity in rotorplane (U

_d

) is mean of free stream

velocity (U

₁

) and the wake velocity (U

₄

)

Conservation of momentum Conservation of energy



U

U



F

_ax

m



₁



₄



2 4 1 U U U_d  



U

U



U

U



F

ax

U

d

m







_{4 1 4} 1

2



Express F

_ax

and P in axial induction factor a

Define induced velocity (axial component) u_i and write U₁ = V_w U_d = U₁ - u_i= V_w - u_i Define axial induction factor a:

Then: w i w i

_u

_aV

V

u

a



;































R w w





R w R w w R w w w R w ax R w R d w w w w w w w w w d w w w d A a a ρV a aV A a V U U m P A a a V a V A a V a V V A a V U U m F A a V A U m a aV a a V a a V V a V V U U a V V a V U U U a V aV V u U U 2 3 2 2 4 2 1 2 4 1 2 2 2 2 2 2 2 2 2 2 4 2 1 1 4 1 1 1 2 ) 1 ( 4 1 2 ) ( 2 1 2 2 ) 1 ( ] 2 1 [ ) 1 ( ] [ 1 ) 1 ( 4 ) 4 4 ( ) 4 4 1 ( 2 1 2 1 ) 1 ( 2 2 1                                               r r r r r r   

Next define an Axial force Coefficient and Power Coefficient

Axial force Coefficient (C

_D,ax

or C

_T

) and

Power Coefficient (C

_P

):









2 3 2 1 2 3 3 2 1 2 2 1 2 2 2 1 ) 1 ( 4 1 2 ) 1 ( 4 1 2 a a A V A a a V A V P C a a A V A a a V A V F C R w R w R w P R w R w R w ax Dax           r r r r r r

The axial force coefficient and the power coefficient

of an actuator disc are a function of a only

From conservation laws:

Maximum Cp found by differentiating with respect to

a:





 

2 1 4 1 4 a a C a a C P Dax    

 

 

 

 

 



13 2 2 2 2 2

0

3

1

1

0

3

4

1

0

2

2

2

1

0

1

2

1

0

1

8

1

4

0



















































a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

da

dC

_P

The maximum value of C

_P

Values of C

_P

and C

_T

at maximum energy

extraction condition:

9

8

)

3

1

1

(

3

1

4

)

1

(

4

5926

.

0

27

16

)

3

1

1

(

3

1

4

)

1

(

4

max , , 2 2 max ,























a

a

C

a

a

C

p C at Dax p

C

_Pmax

= 0.5926 is the maximum of Betz!

We should call the Betz maximum the Betz-Youkowsky maximum, see G. van Kuik: The Lanchester–Betz–Joukowsky Limit

How can the Betz (Lanchester/Youkowsky) maximum be explained:

Force times velocity should be maximum!

2 Extremes:

V V V 1/3.V V= 0 V 2/3.V

Complete blockage: Maximum force but local velocity equals zero

Completely transparant, no blocking:

Maximum velocity but Force equals zero

In between these extremes, an optimum situation exists

The maximum is reached when

V_d is 2/3 V and V₄ = 1/3V

Results -2

Fill in a =1/3 to find the values of C

_P

and C

_T

at maximum energy

extraction condition:

Betz maximum

9

8

,

27

16

max , , max ,



DaxatC_p



p

C

C

Note

1.In literature the Betz maximum is often derived from the Bernouilli equation : • Bernouilli: p + 0.5 r V2 _{= constant.}

• Since Bernouilli is derived from the conservation of energy it does not make any difference

Characterisation of rotor through Power coefficient C

_P

(Note the difference between mechanical and electrical C

_P

)

)

(

27

16

,

_max 3 2 1

V

A

C

Betz

P

C

_P R p



_r



D

Rotor shaft torque T, rotational speed  Mechanical power P_mech = T Ω

Electrical power (generator): P_el = V I cos Φ

Velocity V Rotor Area A_R = π /4 D2 Power coefficient = turbine power wind power

(a = 1/3)

24

Example: Maximum power output

•

_{Calculate maximum mechanical power for:}

–

_{Wind speed V = 10 m/s}

–

_{Diameter D = 100 m}

–

_{Sea level}

•

_Answer:

–

_{Sea level: r = 1.225 kg/m}

3

–

_{D = 100 m: Rotor area A}

_R

_{= π/4 D}

2

_{= 7850 m}

2

–

_{Maximum power:}

P

_max

= C

_P,max

0.5 ρ V

3

_A

R

= 16/27 0.5 1.225 10

3

_{7850 = 2836793 W  ~ 2.8 MW}

NOTE

–

_{In practice: C}

_P

_{< 16/27 (0.59): C}

_p,mech

_{~ 0.5  C}

_P,el

_<0.5

The power coefficient (C

_P

) as function of tip speed ratio (l) is one of the

most important performance characteristics of a wind turbine

Free stream wind speed

Tip speed (m/s)

= Ω (in rad/s) x Blade length (m)

Jos Beurskens

Tip speed ratio (l)= Tip speed

Free stream wind speed

Tip speed ratio λ

• Tip speed of a wind turbine is usually in the order of 75 m/s

(=270 km/hr!!)

Note that the limitation of 75 m/s is mainly because of noise constraints):

• Large turbine (D = 100 m): 15 rpm

• Small turbine (D = 10 m): 150 rpm

(Note: • 1 revolution = 2π rad • 1 minute = 60 sec • 1 rpm = 2π/60 = ~0.1 rad/s)

• So the tip speed for small wind turbines is about the same as the

tip speed for a large wind turbine but they make much more

revolutions per minute

• For such tip speed the tip speed ratio is 7.5 at a free stream

wind speed of 10 m/s

Representative C

_P

-

λ curve

(Source TUDelft)

• C

_pmax

• Corresponds to

a ~ 1/3

• Hence C

_pmax

is still reached

at a

_Betz

even

though C

_pmax

<C

_PBetz

C

_PBetz

0.59

28

Contents

•

Principles of energy extraction, Betz-Lanchester

optimum

•

Design loads

•

Technology, state of the art

•

Wind Farm effects

•

Operation and Maintenance for Off-shore farms

• If you design a wind turbine the

DESIGN LOAD

SPECTRUM

should be calculated

• This represents the loads as experienced by a wind

turbine over its lifetime of 20 years.

• The (expected) external (wind) conditions are input to

these calculations.

• These external wind conditions are dictated by the

standards (usually IEC) and they are defined for

different wind speed classes with main parameters:

•

The (unknown) extreme wind speed over 50 years which is

assumed to be 5 times the (known) annual mean wind speed

•

‘Turbulence intensity’ (a measure for the variations in wind

speed)

DESIGN LOAD SPECTRUM

Definition of wind speed classes according to the

standard IEC 61400 ed.3

V_ref: 10 minute extreme over 50 years V_ave (hub height )= 0.2 V_ref

A,B and C designate the categories for high, medium and low turbulence characteristics I_ref is the expected value of the turbulence intensity at 15 m/s

Example: You measured at your site: V_ave at hub height = 8.2 m/s and a turbulence intensity of 13% V_ref = 5*8.2 = 41 m/s Class IIB

32 Turbine loads are determined by:

• aerodynamic and gravity forces

• structural dynamics of entire wind energy converter • rotor mass imbalance

• aerodynamic rotor imbalance

Turbine loads have to be determined over the

entire liftetime of a wind turbine (20 years) with an aero-elastic design code

Consider all operational conditions during the lifetime

(dictated by standards and determined by wind speed class): • normal operation (power production)

• start and stop (at V_cut-in and V_cut-out) • standstill

• failure (e.g. extreme yaw)

Design load spectrum

Loads calculated with

aero-elastic design code

Stochastic wind simulator

Turbulent characteristics (determined by wind class)

Aeroelastic code

V(y,z,t)

load

time Aeroelastic model description

Control model

Example of turbulent wind field calculated with

ECN’s stochastic wind simulator SWIFT

Calculation of a design spectrum

Short term

for each mean wind speed U (10 min.) repeat ~ 6 times (turbulence is stochastic!)

Long term

lifetime (20 years) Turbulence (U, I) random sea waves and current from Weibull distribution of U U m/s Nr 4-6 1.6e5 …. …. 8-10 1.7e5 …. …. 23-25 3.3e3 0 100 200 300 400 500 600 -3 -2 -1 0 1 2 3 4

load time history

• Sum all 10 minute time series over the lifetime using the Weibull

distribution

• Add special load cases

•  representative load time history over the lifetime

Force distribution on rotor blades

Aerodynamic forces in rotor plane are exerted by the moving

blades:

W

Wind speed

W













 





 

 

Torque

Power

rdr

f

Torque

rdr

f

M

rdr

f

M

dr

f

T

Thrust

blades R ip R ip inplane R oop plane of out blades R oop 3 ₀ 0 0 0 f_oop f_ip

Note:

• f_ip is ‘in-plane’ force;

f_oop is ‘out-of-plane’ force;

• M_ip is often called lead-lag or edgewise moment. Note M_ip is mainly driven by gravity forces

• M_oop is often called flap or flatwise moment

M

_ip

Long-term...fatigue loading of a rotor blade

Long-term...fatigue loading of a rotor blade

Long-term...fatigue loading of a rotor blade

Long-term...fatigue loading of a rotor blade

Max. flap moment Max. edge moment Min. flap moment Max. edge moment

(opposite direction) F la p m o m e n t Edge moment

Long-term...fatigue loading of a rotor blade

Long-term...fatigue loading of a rotor blade

Long-term...fatigue loading of a rotor blade

Long-term...fatigue loading of a rotor blade

F la p m o m e n t Edge moment

5-2-2019

41

https://upload.wikimedia.org/wikipedia/common s/6/61/De_Ambtenaar%2C_de_hoogste_windm olen_van_Europa_staat_bij_Medemblik._Zicht_

vanaf_de_MS_Friesland_03.jpg

Load on blade comparable to…

Load on blade comparable to…

Examples of external loads as function of time

for wind turbines

turbulence, gusts

wind shear

yaw

gravity loads on the

rotating blades

time time time

load

Blade load

load

T=2π/Ω

Courtesy: Wim Bierbooms

Contents

•

Principles of energy extraction, Betz-Lanchester

optimum

•

Design loads

•

Technology, state of the art

•

Wind Farm effects

•

Operation and Maintenance for Off-shore farms

Types

Jos Beurskens

• C

_p,max

is more or less the same for all turbines but note:

• A Savonius turbine is a cheap but inefficient drag machine • The classical wind turbine has inefficient blades

• Some of the aerodynamic losses decrease with  where others increase with decreasing number of blades

Characterization of Rotors

P = T.Ω

(Remember: T = torque)

C

_P

=

P

½.ρ.V

3

_.A

r 45

Characterization of Rotors

2 4 6 8 10

λ = 1

λ = 3

λ = 8

λ > 15

Hence:  increases with decreasing number of blades!!

(Noisy like a jet fighter!)

Will the Vertical Axis Wind Turbines (VAWT) win?

•

Some people think that

VAWTS are economically

feasible at > 8MW

–

Generator down

–

No yawing system

–

No periodic variation of

gravity loads (although

variation of aerodynamic

loads is larger)

Source:Wikipedia

High altitude wind: kites or airplanes?

High altitude wind: kites or airplanes?

High altitude wind: kites or airplanes?

High altitude wind: kites or airplanes?

●

https://www.youtube.com/watch?v=NhoYL8xGRN

8&t=59s

Main characteristics of a horizontal

axis wind turbine

AREVA's 5 Megawatt Offshore movie

http://www.youtube.com/watch?v=6tM9wsOcEBM

Another one at:

http://www.youtube.com/watch?v=LNXTm7aHvWc

Main characteristics -1

•

_{Tower: Slightly conical steel tower, dimensioned}

by overturning moment of rotor axial force

•

Yaw system between tower and nacelle, to yaw

rotor into the wind. Electrical or hydraulical, with

brakes. Controlled by wind vane on nacelle

•

_{Support structure for drive train, leads loads over}

yaw system to tower

•

_{Drive train}

–

With gearbox: main shaft between rotor hub and

gearbox, high speed shaft between gearbox and 2

pole-pair generator

–

_{‘direct drive’, no gearbox, but very large, slow,}

multipole generator

•

_{Electrical frequency converter to enable}

variable speed operation (AC-DC-AC)

•

_{Rotor with three blades (composites, glas fibre}

epoxy or polyester) and pitch control with

electrical or hydraulic drives.

•

Cooling system for gearbox and generator

Main characteristics -2

REpower 5M with gearbox

Hub Rotor Bearings

Gearbox Converter

Transformer Generator Yaw System

Onboard-Crane

M

The nacelle, systems and components,

Repower 5M

Nacelle of direct drive wind turbine

Wind Turbine with Direct Drive

Generator

Enercon

E126

Number of blades

o First it should be known that more blades yield the maximum C

_P

at a lower rotational speed

o 2 bladed rotor: relatively high Ω hence low torque and drive train

loads (P=TΩ) and a relatively low gear ratio for electricity

generating turbines with Ω

_gen

= 1500 rpm

Gear box Gear ratio: Ω_generator/Ω_rotor Ω_rotor~10-20 rpm Ω_generator ~ 1500 rpm 58

Why 3 blades instead of 2 blades *)

•

Pro’s 3 blades

–

_{Lower rotational speed Less noise}

–

Better visual impact

–

‘Smoother’ loading over a revolution

•

Pro’s 2 blades

–

Higher rotational speed lower torque, smaller gear ratio

–

Less blades( lower costs)

•

Conclusion: 2 Bladed turbines may be preferred from a

technological/economical point of view but they will

never be sold (at least not for on-shore conditions,

they may be an option for off-shore

*) Note: Multi-bladed water pumpers have a very low W and hence a

(desirable) high torque (P=WQ)  water pumpers

Contents

•

Principles of energy extraction, Betz-Lanchester

optimum

•

Design loads

•

Technology, state of the art

•

Wind Farm effects

•

Operation and Maintenance for Off-shore farms

(Off-shore) farms

• Example:

– Hornsrev windfarm (DK) on a humid day

• Wind farm effects: – Losses

 wind farm efficiency 85-95% – Increase in mechanical loading on

turbines in farm u increased turbulence reduced windspeed turbine wake Wind farm effects dependent on wind direction:

– Five 2.5MW research turbines N80 with one 108m high meteorological mast

– Five locations for prototype turbines with meteorological masts (108m)

– Measurement Infrastructure – Measurement Pavilion

ECN Wind Turbine Test site Wieringermeer (EWTW)

- Scale Wind farm

Intermezzo: ECN Wind Turbine Test Site Wieringermeer

ECN Wind Turbine Test site Wieringermeer, EWTW

– State of the art turbines – Research farm

– Turbine data available

See also:

http://www.youtube.com/watch?v=mhSOeF6-ut8

Contents

•

Principles of energy extraction

•

Fundamental Equations, momentum theory for

an actuator disk

•

Betz-Lanchester optimum

•

Design loads

•

Technology, state of the art

•

Wind Farm effects

•

Operation and Maintenance for Off-shore farms

www.we-at-sea.org

What makes offshore

different from onshore ?

Offshore WE technology: What makes it different

from land based applications?

• Cost breakdown

• External conditions

(waves, salt conditions, turbulence, extreme winds, (sea) bottom)

• Support structures

• Transport and Assembly

• Commissioning

• Operation and Maintenance; Access

• Grid integration

• Scale & Risk

• Nature issues & Safety

2012-05 www.we-at-sea.org 66

Specific Offshore issues

Why is O&M offshore so difficult?

Availability

of off-shore wind farms

Availability = f (reliability, accessibility)

Availability

100% accessibility (onshore) 80% accessibility 60% accessibility 40% accessibility (exposed offshore) 50 60 70 80 90 100

state-of-the-art improved highly improved

Reliability of design [-] O W EC S A va ila b ili ty [ % ]

Strategy 1

Ampelmann: 2 H_s= 2 m, 50 m vessel (85 %) 69

Johannes Christiaan Schotel, Stormy weather- 1813

Edward William Cooke, 1811-1880

Offshore

Peace and quiet…

So why is offshore O&M so difficult and

expensive?

http://www.youtube.com/watch?v=i9sBA3JGWj4

Personnel & Spare Parts: > 2 – 5 k€ / access

(80 – 120 k€ / day)

Availability/accessibility

www.we-at-sea.org

Operation and Maintenance

Access technology

Photo: Jos BeurskensFoto: Jos Beurskens

Foto: Jos Beurskens

Ampelmann concept

Availability/accessibility: Ampelmann

(J. vd Tempel)

www.we-at-sea.org 77

Operation and Maintenance

Reliability: Components, damaged

Data, timeseries 0.0 5.0 10.0 15.0 20.0 25.0 0 30 60 90 120 150 180 210 240 270 300 Time [hrs] W in d sp ee d [m /s ] 0.00 1.00 2.00 3.00 4.00 5.00 W av e he ig ht [ m ]

Wind speed [m/s] (Upper limit) Vref

Hm0 [m] (Upper limit) Href

Failure

Repair time for mission of 40 resp. 20 hr?

Hs = 1,5 m Vw = 12 m/s

T_wait_{40 hr} = 96 hr in operation:136 hr

In Operation

T_wait _{20 hr} = 56 hrin operation:76 hr

In Operation

Availability/reliability (O&M)

ECN; Braam, Rademakers

Summary and conclusion

•

_{Wind Energy is useful, fun and technologically}

very challenging

•

_{Good prospects for both experienced and}

unexperienced young people

–

So join the club!

Questions ??